Space of modular forms of level 660, weight 2, and Character 660.x

• Label: 660.2.x
• Level: $660$
• Weight: $2$
• Character orbit: 660.x
• Rep. character: $\chi_{660}(373,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.x (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(660, [\chi])\).

	Total	New	Old
Modular forms	312	24	288
Cusp forms	264	24	240
Eisenstein series	48	0	48

Trace form

\( 24 q + 8 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(660, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
660.2.x.a	$660$	$2$	660.x	55.e	$4$	$24$	$12$	$5.270$		None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(660, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(660, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)